New figures show that mortality at the Western General is significantly lower than the national average.
Across the country, rates have fallen by 4.5 per cent over the past two years.
The Scottish Patient Safety Programme was set up with the aim of reducing mortality by 20 per cent by the end of 2015, a target that was missed by 3.5 per cent.
A new target has now been set to cut death rates by a further ten per cent by December 2018.
Health Secretary Shona Robison said: “It is encouraging to see that our commitment to patient safety across the health service is delivering such strong results, especially at a time when our NHS is treating more people, with more complex needs, than ever before.
“The 4.5 per cent drop in mortality rate since the start of 2014 shows we are making progress towards our new aim of a ten per cent reduction by December 2018. This is on top of the improvements in mortality already achieved since the start of the Scottish Patient Safety Programme in 2007.
“Scotland was the first country in the world to implement a national patient safety programme and is the only UK country publishing and driving improvement in our NHS through the use of mortality data in this way.”